The theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in many areas of statistics, economics, and mathematical finance. They can often be written in the form of a Bellman equation, and are therefore often solved using dynamic programming. Results on optimal stopping were first developed in the discrete case. The formulation of optimal
stopping problems for discrete stochastic processes was in sequential analysis, an area of
mathematical statistics where the number of observations is not fixed in advance but is a random
number determined by the behavior of the data being observed.
[1]} was the first person to come up with results on optimal stopping theory for stochastic
processes in discrete time.
We refer to the book of [2]} for a comprehensive review on different aspects of optimal stopping problems.
